<h2>Problem 242</h2>
<div style="color:#666;font-size:80%;">25 April 2009</div><br />
<div class="problem_content">
<p>Given the set {1,2,...,<var>n</var>}, we define <var>f</var>(<var>n</var>,<var>k</var>) as the number of its <var>k</var>-element subsets with an odd sum of elements. For example, <var>f</var>(5,3)&thinsp;=&thinsp;4, since the set {1,2,3,4,5} has four 3-element subsets having an odd sum of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.</p>

<p>When all three values <var>n</var>, <var>k</var> and <var>f</var>(<var>n</var>,<var>k</var>) are odd, we say that they make <br />
an <i>odd-triplet</i> [<var>n</var>,<var>k</var>,<var>f</var>(<var>n</var>,<var>k</var>)].</p>

<p>There are exactly five odd-triplets with <var>n</var>&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;10, namely:<br />
[1,1,<var>f</var>(1,1)&thinsp;=&thinsp;1], [5,1,<var>f</var>(5,1)&thinsp;=&thinsp;3], [5,5,<var>f</var>(5,5)&thinsp;=&thinsp;1], [9,1,<var>f</var>(9,1)&thinsp;=&thinsp;5] and [9,9,<var>f</var>(9,9)&thinsp;=&thinsp;1].</p>

<p>How many odd-triplets are there with <var>n</var>&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;10<img src="" style="display:none;" alt="^(" /><sup>12</sup><img src="" style="display:none;" alt=")" />&thinsp;?</p>
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